Parametric frequency conversion of ultrashort light pulses

A study is made of the evolution of ultrashort pulses of interrogation and generated fields, traveling across a medium after a pump pulse under two-photon resonance conditions. It is shown that, in spite of the absence of overlap of the pulses in space and time, the generated wave becomes phase-locked. The area theorem is obtained for the process in question. It is found that at large distances the second pulse should give rise to a subpulse of the interrogation field and a proportional subpulse whose area tends to zero or to $2\pi$. This conclusion about the formation of subpulses and their limiting areas applies also in the two-photon interaction case. A report is given of an estimate of the threshold intensities of an interrogation pulse in cesium and sodium vapors. The maximum conversion efficiency is found as a function of the pump energy, parameters of the investigated medium, and frequencies of the interacting fields. It is shown that an overall conversion efficiency close to 100% can be obtained when the intensities of the pump and interrogation fields are within the capabilities of the currently available lasers.